Ben Shelef, CEO of the Spaceward Foundation (host of the Space Elevator Games) responded to a question about how strong a space elevator tether has to be. With Ben’s help, I wrote a 3-part series about this earlier (Part 1, Part 2 and Part 3) and Ben has augmented this by discussing the proper units to use in describing the strength of a Space Elevator tether;
How strong does a Space Elevator tether need to be? Many numbers are bandied about, and usually with a designation of GPa (Giga-Pascals) as their unit of measure. However, a GPa figure is meaningless without a density figure to go with it.
The metric at question is GPa/(g/cc), or specific strength – strength-per-density. The textile industry, which often deals with specific strength of materials, uses the unit of N/Tex. If you work out the units, a N/Tex turns out to be exactly equivalent to a GPa/(g/cc), a Tex… We propose to give this unit a proper name – in the metric system, we define 1 Yuri = 1 Pa/(kg/m3), and so a GPa/(g/cc) or a N/tex are equal to 1 MYuri (Mega Yuri).
Why is strength (GPa) not a good unit to evaluate the material with?
Think about it this way – if you pull on a garden hose and it breaks at 100 lb, and if the diameter of the hose is such that its area is 2 square inches, can you say that the rubber failed at 50 PSI? Of course not – the hose is mostly air, only the wall of the hose is holding the force. you should use the area of the wall, not the hose.
In exactly the same way, if 12 inches of the garden hose weighs a pound, can you say that the density of the rubber is 1/24 [lbs/in3] ? Of course not – only the wall of the hose has weight.
BUT!!! You can safely say that the *specific strength* of the rubber is 50/(1/24)=1200 PSI/(lb/in3) and you don’t have to even measure the diameter of the hose – just divide the breaking force (100) by the linear mass density (1/12), and you get the same exact number (1200). The cross-sectional area canceled out, and the only two things we need to measure is the breaking *force* (in lbs) and the weigh-per-linear-inch. Hence N/Tex.
So back to Space Elevators:
Computer simulations of CNTs cap the specific strength of individual tubes at between 40 and 50 MYuri. Practical measurements seem to converge on that number as well. The density of Carbon Nanotubes is 2.2 g/cc, so using this density the proper strength figure is 88-110 GPa. Remember though, it’s the 40-50 MYuri figure that’s the deal maker.
We can build a Space Elevator using a 40 MYuri material. Even 30. It’s just that the lower the specific strength, the heavier the ribbon, and the more powerful our motors have to be. (How are motors connected to the tether strength? See the discussion about the Space Elevator Feasibility Condition) If we go below 30 MYuri, the power system starts to look impossible.
There’s a whole discussion about safety margins that needs to factor in here. If the CNTs are 45 MYuri, and the cable is 40 MYuri, how much can we really load it at? 30 MYuri? this means we have a safety margin of 10/30, or 33%. Since the loading of the Space Elevator structure is incredibly predictable (more so than most any other structure ever built) we think this margin is sufficient, but this is a topic for another post.
The document that Ben refers to, the Space Elevator Feasibility Condition, should be required reading for anyone who wants to understand how viable a Space Elevator is.